Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}5x+3y &= -7 \\ 2x+y &= -5\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $2x = -y-5$ Divide both sides by $2$ to isolate $x$ $x = {-\dfrac{1}{2}y - \dfrac{5}{2}}$ Substitute this expression for $x$ in the first equation. $5({-\dfrac{1}{2}y - \dfrac{5}{2}}) + 3y = -7$ $-\dfrac{5}{2}y - \dfrac{25}{2} + 3y = -7$ Simplify by combining terms, then solve for $y$ $\dfrac{1}{2}y - \dfrac{25}{2} = -7$ $\dfrac{1}{2}y = \dfrac{11}{2}$ $y = 11$ Substitute $11$ for $y$ in the top equation. $5x+3( 11) = -7$ $5x+33 = -7$ $5x = -40$ $x = -8$ The solution is $\enspace x = -8, \enspace y = 11$.